12 1 Lines That Intersect Circles Warm Up

12 -1 Lines That Intersect Circles Objectives Identify tangents, secants, and chords. Use properties

12 -1 Lines That Intersect Circles Vocabulary interior of a circle exterior of a

12 -1 Lines That Intersect Circles This photograph was taken 216 miles above Earth.

12 -1 Lines That Intersect Circles _______- the set of all points inside the

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Example 1: Identifying Lines and Segments That Intersect

12 -1 Lines That Intersect Circles Example 2: Identifying Tangents of Circles Find the

12 -1 Lines That Intersect Circles Example 2 B Find the length of each

12 -1 Lines That Intersect Circles ______- a line that is tangent to two

12 -1 Lines That Intersect Circles A common tangent is a line that is

12 -1 Lines That Intersect Circles Example 3 A: Using Properties of Tangents HK

12 -1 Lines That Intersect Circles Example 3 B RS and RT are tangent

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12 -1 Lines That Intersect Circles Warm Up Write the equation of each item. 1. FG x = – 2 2. EH y=3 3. 2(25 –x) = x + 2 x = 16 Holt Mc. Dougal Geometry 4. 3 x + 8 = 4 x x=8

12 -1 Lines That Intersect Circles Objectives Identify tangents, secants, and chords. Use properties of tangents to solve problems. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Vocabulary interior of a circle exterior of a circle chord secant tangent of a circle point of tangency congruent circles Holt Mc. Dougal Geometry concentric circles tangent circles common tangent

12 -1 Lines That Intersect Circles This photograph was taken 216 miles above Earth. From this altitude, it is easy to see the curvature of the horizon. Facts about circles can help us understand details about Earth. Recall that a circle is the set of all points in a plane that are equidistant from a given point, called the center of the circle. A circle with center C is called circle C, or C. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles _______- the set of all points inside the circle. _______ - the set of all points outside the circle. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Example 1: Identifying Lines and Segments That Intersect Circles Identify each line or segment that intersects L. chords: secant: tangent: diameter: radii: Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Example 2: Identifying Tangents of Circles Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of R: radius of S: point of tangency: equation of tangent line: Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Example 2 B Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of C: 1 radius of D: 3 point of tangency: equation of tangent line: Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles ______- a line that is tangent to two circles. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles A common tangent is a line that is tangent to two circles. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Example 3 A: Using Properties of Tangents HK and HG are tangent to F. Find HG. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Example 3 B RS and RT are tangent to Q. Find RS. Holt Mc. Dougal Geometry